{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2QD2XO7SGQUPLTYDVF44YBBAWS","short_pith_number":"pith:2QD2XO7S","canonical_record":{"source":{"id":"1602.03996","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-12T10:09:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2f468d06333580450dffa677fa6b0363ad3a37075992826ddb462df0956fec8f","abstract_canon_sha256":"e97539fc00b660daa36740a1db7261a66f2361be899fac4c54b3ddba2256f1bb"},"schema_version":"1.0"},"canonical_sha256":"d407abbbf23428f5cf03a979cc0420b4863097683f80f2464a949bf106fa1729","source":{"kind":"arxiv","id":"1602.03996","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03996","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03996v3","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03996","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"2QD2XO7SGQUP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2QD2XO7SGQUPLTYD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2QD2XO7S","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2QD2XO7SGQUPLTYDVF44YBBAWS","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03996","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-12T10:09:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"2f468d06333580450dffa677fa6b0363ad3a37075992826ddb462df0956fec8f","abstract_canon_sha256":"e97539fc00b660daa36740a1db7261a66f2361be899fac4c54b3ddba2256f1bb"},"schema_version":"1.0"},"canonical_sha256":"d407abbbf23428f5cf03a979cc0420b4863097683f80f2464a949bf106fa1729","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:57.206141Z","signature_b64":"tt9ltigVDPvTjZ+M1/M44eEW7Z3mMBbkBnCJYbDNcFeGHidsv7m1H3eE4KxfTQFJI/uT/UGc2NeWVJKbdLLxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d407abbbf23428f5cf03a979cc0420b4863097683f80f2464a949bf106fa1729","last_reissued_at":"2026-05-18T00:18:57.204739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:57.204739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03996","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/QEdRY0akiDt7sbZXfq7lZ3QmXtp3mMmKnKEsIwEzptgx+v9HWMB8oPJQyRMmpZGvJwcoM2a7lSRsV3/InxSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:29:15.093920Z"},"content_sha256":"52519fdfa36c97e1eceea8b610a40d4932bff1ccd2bc3e82af922e38de3f858e","schema_version":"1.0","event_id":"sha256:52519fdfa36c97e1eceea8b610a40d4932bff1ccd2bc3e82af922e38de3f858e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2QD2XO7SGQUPLTYDVF44YBBAWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cylindrical continuous martingales and stochastic integration in infinite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Ivan Yaroslavtsev, Mark Veraar","submitted_at":"2016-02-12T10:09:54Z","abstract_excerpt":"In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration theory for operator valued processes under the condition that the range space is a UMD Banach space. We obtain two-sided estimates for the stochastic integral in terms of the $\\gamma$-norm. In the scalar or Hilbert case this reduces to the Burkholder-Davis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03996","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+AvmcxHOllsfilvFKmcH6mIIhVShFC0zOCqMjjWFjDj3PBGS+yzDIweDoE80sZbo6YhN0tDGBl4u8bMB7k8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:29:15.094257Z"},"content_sha256":"fcab77365d56a65e37551fc7d8a0242f2023546e04cc66f0b43b6fe098fa8736","schema_version":"1.0","event_id":"sha256:fcab77365d56a65e37551fc7d8a0242f2023546e04cc66f0b43b6fe098fa8736"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/bundle.json","state_url":"https://pith.science/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T10:29:15Z","links":{"resolver":"https://pith.science/pith/2QD2XO7SGQUPLTYDVF44YBBAWS","bundle":"https://pith.science/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/bundle.json","state":"https://pith.science/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QD2XO7SGQUPLTYDVF44YBBAWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2QD2XO7SGQUPLTYDVF44YBBAWS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e97539fc00b660daa36740a1db7261a66f2361be899fac4c54b3ddba2256f1bb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-12T10:09:54Z","title_canon_sha256":"2f468d06333580450dffa677fa6b0363ad3a37075992826ddb462df0956fec8f"},"schema_version":"1.0","source":{"id":"1602.03996","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03996","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03996v3","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03996","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"2QD2XO7SGQUP","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2QD2XO7SGQUPLTYD","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2QD2XO7S","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:fcab77365d56a65e37551fc7d8a0242f2023546e04cc66f0b43b6fe098fa8736","target":"graph","created_at":"2026-05-18T00:18:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration theory for operator valued processes under the condition that the range space is a UMD Banach space. We obtain two-sided estimates for the stochastic integral in terms of the $\\gamma$-norm. In the scalar or Hilbert case this reduces to the Burkholder-Davis","authors_text":"Ivan Yaroslavtsev, Mark Veraar","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-12T10:09:54Z","title":"Cylindrical continuous martingales and stochastic integration in infinite dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03996","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:52519fdfa36c97e1eceea8b610a40d4932bff1ccd2bc3e82af922e38de3f858e","target":"record","created_at":"2026-05-18T00:18:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e97539fc00b660daa36740a1db7261a66f2361be899fac4c54b3ddba2256f1bb","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-12T10:09:54Z","title_canon_sha256":"2f468d06333580450dffa677fa6b0363ad3a37075992826ddb462df0956fec8f"},"schema_version":"1.0","source":{"id":"1602.03996","kind":"arxiv","version":3}},"canonical_sha256":"d407abbbf23428f5cf03a979cc0420b4863097683f80f2464a949bf106fa1729","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d407abbbf23428f5cf03a979cc0420b4863097683f80f2464a949bf106fa1729","first_computed_at":"2026-05-18T00:18:57.204739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:57.204739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tt9ltigVDPvTjZ+M1/M44eEW7Z3mMBbkBnCJYbDNcFeGHidsv7m1H3eE4KxfTQFJI/uT/UGc2NeWVJKbdLLxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:57.206141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03996","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52519fdfa36c97e1eceea8b610a40d4932bff1ccd2bc3e82af922e38de3f858e","sha256:fcab77365d56a65e37551fc7d8a0242f2023546e04cc66f0b43b6fe098fa8736"],"state_sha256":"fafb27c5e726eabcd2dcc5e79d36645a2e5feef852a740f452169c52a5f4b089"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+6RMopbICfFzNaivkWsAV9sjDoov8a8UsJnIeDjHc+hoY0OKBqxVB6sCr9MNyqZfE/fTtyFpGBkbeKLwCKYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:29:15.096180Z","bundle_sha256":"bfc7520746fffc5e63147ab32f50a28588d11be15e28efc81932730f5874b23b"}}